Problem: Which of the following numbers is a factor of 156? ${5,6,9,10,11}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $156$ by each of our answer choices. $156 \div 5 = 31\text{ R }1$ $156 \div 6 = 26$ $156 \div 9 = 17\text{ R }3$ $156 \div 10 = 15\text{ R }6$ $156 \div 11 = 14\text{ R }2$ The only answer choice that divides into $156$ with no remainder is $6$ $ 26$ $6$ $156$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $156$ $156 = 2\times2\times3\times13 6 = 2\times3$ Therefore the only factor of $156$ out of our choices is $6$. We can say that $156$ is divisible by $6$.